Brumbies coach Jake White described his team's victory over the Bulls in the Super Rugby semi-final at Loftus Versfeld in Pretoria as "the greatest win the Brumbies have ever had".

"It's got to be," the Rugby World Cup 2007-winning coach said after five-eighth Matt Toomua had broken the line and slipped a flat pass to centre Tevita Kuridrani for the match-winning try with less than two minutes to play.

"I spoke to [man-of-the-match] George Smith after the game, and he said he's never experienced anything like that in his life," White said.

"We defended and defended, and the law of averages told us we were going to get out of our half and have one crack at getting the win. And then it happened."

The Bulls kicked off having won 22 of their previous 24 home matches against trans-Tasman teams, and all five of their home finals matches, and they were well on track to improve that record late in the game. But Bulls captain Dewald Potgieter controversially turned down three penalty goals to kick for the corner while leading by one point in the final 13 minutes, and he and his team-mates were made to pay in the most cruel fashion.

"They have the best goal-kicker in the whole competition [Morne Steyn] and a new hooker on who has to throw the ball into the lineout, and they decide to go for touch," White said of the Potgieter's decisions. "It's moments like that that change the whole destiny of clubs."

Steyn also sprayed a desperate drop-goal attempt between the second and third turned down penalty shots.

"That's finals football, that's what pressure does to top players," White said.

Bulls coach Frans Ludeke issued a message to take the three points when they were next offered by referee Craig Joubert in the 76th minute, but Potgieter defended his previous decisions. "We tried to spend most of the time in their territory and it was working for us right up until the end when we took that penalty and were back in our own half," he said. "We just couldn't exit from there. We were struggling all night with our exits."

The Brumbies now turn their attention to the Chiefs, who beat fellow New Zealanders the Crusaders 20-19. They'll return to Canberra, remaining there until Wednesday, before travelling to Hamilton for the Super Rugby final at Waikato Stadium.

The Brumbies' finals travel schedule is not quite as gruelling as that of last year's Super Rugby runners-up, the Sharks, but White suggested it would take a toll on his team. "It's going to be an uphill battle that's never been done before," he said. "But there's a lot of things that haven't been done by teams before, and the Brumbies have done them week in, week out."

The Brumbies stunned the Bulls in Pretoria (video available only in Australia)